Structural,mechanical and optoelectronic features of cubic Be$_x$Mg$_{1−x}$S, Be$_x$Mg$_{1−x}$Se and Be$_x$Mg$_{1−x}$Te alloyshave been explored by DFT-based FP-LAPW approach. Nonlinear reduction in lattice constant, but increment in bulk modulus and each of the elastic constants $C_{11}$, $C_{12}$ and $C_{44}$, occurs with increasing Be-concentration $x$ in each system. All the specimens exhibit elastic anisotropy. Specimens at $x = 0.0$, 0.25 and 0.50 show ductility, but remaining specimens at $x = 0.75$ and 1.0 show brittleness. Each ternary alloy is a direct ($\Gamma$−$\Gamma$) band gap ($E_{\rm g}$) semiconductor. Almost linear decrease in $E_{\rm g}$ with increase in $x$ is observed in each alloy system. Ionic bonding exists among the constituents of all specimens. The occupied valence chalcogen-p as initial and unoccupied conduction Be-3s, 2p and Mg-4s, 3p as final states play a keyrole in optical transitions. Nature of variation of zero-frequency limit in each of the $\epsilon_1(\omega)$, $n(\omega)$ and $R(\omega)$ spectra with $x$ isopposite to, while critical point in each of the $\epsilon_2(\omega)$, $k(\omega)$, $\sigma(\omega)$ and $\alpha(\omega)$ spectra with $x$ is similar to, the nature of variation of $E_{\rm g}$ with $x$.

First principle calculations of elastic and thermal properties of zinc-blende specimens within Hg$_x$Zn$_{1–x}$S, Hg$_x$Zn$_{1-x}$Se and Hg$_x$Zn$_{1-x}$Te ternary systems are executed. Elastic stiffness constants decrease non-linearly with increasing Hg-concentration in each system. Each cubic sample is mechanically and dynamically stable, elastically anisotropic, compressible against elastic deformation, ductile and fairly plastic. Hardness of specimens in each system reduces with enhancement in Hg-composition. Mixed kind of bonding with dominancy of covalent over ionic in most cases, bond bending over stretching and central type of interatomic bonding forces are calculated. In each system,covalency, Debye temperature and frequency, Debye temperature for acoustic phonon, thermal conductivity and melting temperature of specimens decreases, while Philip ionicity and Gruneisen parameter increases with enhancingHg-concentration.

Structural, mechanical and optoelectronic features of zinc-blende Cd$_{1-x-y}$Zn$_x$Hg$_y$Se quaternary alloys as well as allied binary compounds and ternary alloys have been investigated through first-principle calculations. Computed elastic stiffness constants ensure that each specimen is mechanically stable, ductile, elastically anisotropic and compressible. The covalent bonding plays a superior role over ionic bonding in each specimen. The phonon dispersion spectra ensure that each binary compound is dynamically stable, while each ternary or quaternary alloy exhibits dynamical instability. Each semiconductor alloy exhibits a direct (${\Gamma}$–${\Gamma}$) bandgap. Electrons possess lower effective mass compared to holes. Electrons excited from the Se-4p state of valence band to Zn-5s, Cd-6s and Hg-7s states of conduction band contribute peaks in dielectric function spectra of the considered specimens. Computed oscillator strength of quaternary alloys reveals availability of adequate number of electrons in respective conduction bands. On the basis of computed optoelectronic properties, the alloys would be suitable to fabricate near-UV and UV optoelectronic devices.